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A207820 Let A = A025584. a(n) is the smallest A(m) such that the interval (A(m)*n, A(m+1)*n) contains no primes from A. 5
2, 2, 2, 1783, 967, 1663, 3187, 4813, 13873, 20347, 1783, 2617, 27743, 14533, 54829, 71143, 66169, 46687, 44119, 57787, 79609, 552883, 21397, 297079, 1187107, 89017, 798697, 285763, 761377, 2660587, 812047, 1463257, 2795059, 2816239, 2676727, 3069607, 2500297 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Conjecture. For n>=3, every a(n) is the lesser of a pair of cousin primes p and p+4, cf. A023200.
The limit of a(n) as n goes to infinity is infinity.
LINKS
MATHEMATICA
Table[aPrime[[NestWhile[#1+1&, 1, !(nextAPrime[n aPrime[[#1]]]>n aPrime[[#1+1]])&]]], {n, 2, 20}]
PROG
(PARI) is_a025584(x) = isprime(x) && !isprime(x-2)
a025584_next(n) = {local(p); p=n+1; while(!is_a025584(p), p=p+1); p}
no_a025584(a, b) = {local(x, r); r=1; for(x=a+1, b-1, if(is_a025584(x), r=0)); r}
a207820(n) = {local(r, rp); rp=2; r=3; while(!no_a025584(n*rp, n*r), rp=r; r=a025584_next(r)); rp} \\ Michael B. Porter, Jan 20 2013
CROSSREFS
Sequence in context: A324302 A216668 A057330 * A186069 A280842 A244442
KEYWORD
nonn
AUTHOR
EXTENSIONS
a(21)-a(37) from Michael B. Porter, Jan 20 2013
STATUS
approved

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Last modified April 18 06:08 EDT 2024. Contains 371767 sequences. (Running on oeis4.)